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Talks at this conference

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Prof. Andrew Bacon (USC) will give a masterclass on Higher-Order Metaphysics at King’s College London on May 8th-10th, 2019. The masterclass will include guest talks by Nick Jones (Birmingham), Jessica Leech (KCL), and Timothy Williamson (Oxford).

The event is open to graduate students and researchers from any institution.

Presentation

Some central questions of metaphysics revolve around propositions, properties and relations and around how they interact with modality: What does it mean for a necessity to be broader than another? Is there such a thing as a broadest necessity? what does it mean for a property or relation to be fundamental? Are fundamental properties and relations `freely recombinable’ in the sense that they can instantiate any logically consistent pattern? Are propositions structured entities constructed out of fundamental properties and relations? More generally, to what extent can we make good on the metaphor of reality as a language, and the corresponding metaphor of the fundamental as the primitive constants of that language?

Unfortunately, debates on such questions are often formulated in ways that are prone to lead to paradoxes. Higher-order logic is a precise framework for regimenting such debates. It is a generalization of first-order logic that allows one to quantify not just into singular position but into any given grammatical position. It allows one to replace quantification over propositions, properties and modalities by quantification into sentence, predicate or operator position. Higher-order logic is often studied in a broadly Fregean setting which in effect assumes that there are only two propositions. Once this assumption is lifted there are a surprising number of choice points regarding the logic and model theory of higher-order logic, corresponding to a number of different metaphysical pictures of the granularity of properties and propositions. Many of the technical tools in this area have been developed by computer scientists and category theorists but aren’t widely known to philosophers.

This masterclass will present these ideas in a way that is accessible to philosophers, and tailored to their concerns. The first half of the series will cover general technical machinery needed for modelling higher-order logic. The second half we will apply these tools to the metaphysical questions raised above.